The information pertaining to the relative positions of atoms near the surface of a sample is important in understanding the chemical and physical properties of surface structure. Techniques of gathering information concerning surface structure include localized source electron diffraction, such as photoelectron, Auger, and Kikuchi diffraction, low energy electron diffraction (LEED) and diffuse LEED (DLEED). A localized source electron is an electron that either appears to, or actually does, originate near an atomic nucleus within the sample.
In order to obtain three dimensional information regarding lattice structure it has been suggested to use holograms and holographic techniques (the creation of a three dimensional image from an interference pattern). A hologram is a record of an interference pattern, which, when properly processed, forms a three dimensional image of the object originally used to create the interference pattern. Thus, assuming that it is possible to create a practical process of reproducing the image, a hologram of a surface may be used to determine the relative positions of the atoms near the surface of the sample.
The use of localized-source electron holography to gather information concerning surface structure promises to be a great advance in the art. It has been suggested, for example, that, an electron hologram can be created by recording the intensity of an interference pattern formed by electrons which are emitted from an atom in the sample, and travel to the film directly from this atom (the reference wave), or after scattering off of one or more nearby atoms in the sample (the object wave). Then, rather than physically illuminating the hologram with an electron beam to reconstruct the image, data corresponding to the reconstructed intensity is generated by multiplying the recorded interference data by a function representing the intensity of a reconstructing wave, i.e. "mathematically" illuminating the hologram to reconstruct a real image. The image intensity at points off the hologram, i.e. a reconstructed image, may then be appropriately determined via a computer using certain mathematical techniques. Such a method of holographic DLEED imaging is described in Saldin et al., Phys. Rev. Lett. 64:1270 (1990).
A further method of using holographic techniques to determine surface structure is set forth in Photoelectron Holghraphy, Vol. 61, No. 12, Phys. Rev. Letters, Sept. 19, 1988, by John Barton, which proposed to interpret photoelectron (PhD) data collected on a portion of a spherical surface centered about a crystal having adsorbed atoms as a photoelectron hologram. It was suggested that the photoelectron data may be normalized by subtracting from each intensity data point the intensity of the reference wave, and then dividing this difference by the square root of the intensity of the reference wave. Next, the normalized data, which corresponds to the intensity of a hologram, is then multiplied by a function representing a reconstructing wave, which is the conjugate of the reference wave, in this case a converging spherical wave. The resultant data corresponds to the transmitted intensity of an illuminating wave. The intensity at points off of the hologram (the spherical surface) is calculated using a mathematical technique called the Helmholtz-Kirchoff integral.
The Helmholtz-Kirchoff integral is a well known technique of determining the intensity of light in three dimensions given the intensity on a surface, and is particularly useful in PhD applications. According to the Helmholtz-Kirchoff integral, each point on the surface is treated as a point source of light, and a mathematical expression for the intensity in three dimensions due to each individual point source is determined. A mathematical expression for the total intensity in three dimensions is simply the sum of the amplitudes due to the point sources, and may be found by integrating the function representing the amplitudes due to the individual point sources over the surface (i.e. the point sources). The Helmholtz-Kirchoff integral, when applied to PhD holographic data, is in the form of a double Fourier integral, and may be solved numerically using a fast Fourier transform. A second method of reconstructing three-dimensional images from the normalized data is to apply three-dimensional Fourier transformation to the data. Three-dimensional images can also be formed from an interference pattern made up of a multitude of holograms. This is the case in spectroscopy X-ray photoemission, for example, when the sample orientation is rotated.
Known methods of three-dimensional atomic imaging suffer from poor resolution and accuracy. In particular, a resolution to 2-3 angstroms is insufficient when the atoms and bond lengths being observed are of comparable size. The present invention addresses these problems.